WASHINGTON/MEXICO CITY (REUTERS, AFP) - US President Donald Trump on Thursday (Jan 26) said his Mexican counterpart Enrique Pena Nieto should cancel his upcoming visit to Washington if Mexico refuses to pay for a wall along the border.

"The US has a 60 billion dollar trade deficit with Mexico. It has been a one-sided deal from the beginning of Nafta with massive numbers... of jobs and companies lost. If Mexico is unwilling to pay for the badly needed wall, then it would be better to cancel the upcoming meeting," Trump said on Twitter.

Trump has ordered work to begin on building a wall along the Mexican border, angering his southern neighbor with his hardline stance on immigration.

A possible cancellation of the summit planned next week between Pena Nieto and Trump would fuel uncertainty, Mexican Finance Minister Jose Antonio Meade said on Thursday.

"That's correct," Meade said on Mexican radio when asked if a cancellation of the meeting would fuel uncertainty.

The US leader instructed officials on Wednesday to begin to "plan, design and construct a physical wall along the southern border" and see how it could be funded.

"A nation without borders is not a nation," Trump said, echoing former president Ronald Reagan, as he visited the Department of Homeland Security to sign two executive orders. "Beginning today, the United States of America gets back control of its borders," the Republican president said.

Hours later, Pena Nieto demanded "respect" for his country in a nationally televised address.

"I regret and condemn the decision of the United States to continue construction of a wall that, for years, has divided us instead of uniting us," Pena Nieto said. "I have said it time and again: Mexico will not pay for any wall."

Pena Nieto said he would wait for a report from a high-level Mexican delegation in Washington and consult with governors and lawmakers before deciding on "the next steps to take."

Lawmakers are pressuring the Mexican leader to cancel a meeting with Trump in Washington scheduled for next week.

Stemming immigration was a central plank of Trump's election campaign. His signature prescription was to build a wall along the 3,200km US-Mexico border.

Some of the border is already fenced, but Trump says a wall is needed to stop illegal immigrants from Latin America.

A Morning Consult/Politico poll released Wednesday said 47 per cent of voters support building a wall, with 45 per cent against.

Experts have voiced doubts about whether a wall would actually slow illegal immigration, or if it is worth the billions it is expected to cost.

"I suspect that a lot of Trump supporters would be just as happy with a big statue of a middle finger pointed south," said Congressman Luis Gutierrez.

"Both are about equally effective as national security strategies."

Despite the high-octane rhetoric, Trump's action was piecemeal, looking to identify existing funds that could be diverted toward the project. The Republican-controlled Congress, which has long preached fiscal prudence, would need to approve billions of dollars more if the wall is to be anywhere near completed.

Trump also ordered a survey of the border to be completed within 180 days.

Much of the land needed to build the wall would have to be seized from private citizens in Texas, the state of Texas or tribal authorities. That could result in long court battles and hefty expropriation payments.

"The only real solution to reform our immigration system is to pass comprehensive immigration reform that provides a path to citizenship for the 11 million" undocumented people in the United States, top Senate Democrat Chuck Schumer said.

Trump has promised to make Mexico pay for the wall, something the Mexican government has said will not happen.

"Ultimately it will come out of what's happening with Mexico, we're going to be starting those negotiations relatively soon. And we will be, in a form, reimbursed by Mexico," Trump said in an interview with ABC News.

Trump aides have considered raising border tariffs or border transit costs as one way to "make Mexico pay." Another threat is to finance the wall by tapping into remittances that Mexican migrants send home, which last year amounted to $25 billion.

"There are a lot of different ways of getting Mexico to contribute to doing this, and there are different ways of defining how exactly they pay for it," House leader Paul Ryan said in an interview on MSNBC, while also conceding that the United States is "going to pay for it and front the money up."

Left unresolved is the fate of the "dreamers," the foreign-born, US-raised children of undocumented migrants. The children - many of whom are now adults - were brought to the United States illegally as minors.

Some 750,000 of them were granted work permits and temporary residency under a 2009 programme known as DACA under former president Barack Obama.

Trump blasted DACA on the campaign trail, but in the ABC News interview he seemed to soften his position.

"They shouldn't be very worried," Trump told ABC. "I do have a big heart. We're going to take care of everybody. We're going to have a very strong border. We're gonna have a very solid border. Where you have great people that are here that have done a good job they should be far less worried."

Trump promised that his administration will "be coming out with policy on that over the next three to four weeks," but gave no further details.